一类 Rn 上半线性椭圆方程有界正解 的存在性和对称性

本文研究 Rn 上型如下列具有次线性项加超线性项椭圆方程: - Δu = a(x ) (λ us + up ) , x∈ Rn , 其中 ,n≥ 3, 0 < s < 1 < p,λ > 0为参数.用上下解方法给出了方程有界正解存在性及多解性结果.用移 动平面方法给出解的径向对象性结果 .

On the existence and symmetry of bounded positive solut ion of semilinear ellipt ic equtions in Rn

In this paper, the following semilinear elliptic equation with sublinear and superlinear nonlin earities w as studied : - Δu= a(x ) (λ us+ up ) ,　x∈ Rn , where n≥ 3, 0< s < 1< p,λ > 0 is a parameter. Using subsup-solution method, the results on existence land multiplicity of bounded positive solutions were presented. Using“ Moving-plane” method, a result on the symmetry of bounded positive solutions was also presented.